1. Field of the Invention
This invention relates to a logarithmic amplification circuit.
2. Description of the Prior Art
A logarithmic amplification circuit shown in FIG. 1 is well-known as a conventional one, which is a logarithmic amplification circuit described in the Plessey Corporation's Catalogue SL521, and comprises a differential amplifier consisting of transistors TR1 and TR2 as a first stage and a half-wave rectifier consisting of a differential transistor pair TR4 and TR5 only one transistor of which has an emitter resistor RE (the emitter resistor RE is connected to the transistor TR5 in FIG. 1) as a second stage. The operational principle thereof will be explained below.
In FIG. 1, if an electric current to be flowed into a resistor R1 is expressed as I0, a voltage to be applied between the transistors TR4 and TR5 is expressed as VB4,5, base voltages of the transistors TR4 and TR5 are respectively expressed as VBE4 and VBE5, collector currents of the transistors TR4 and TR5 are respectively expressed as Ic4 and Ic5 and its current amplification factor is expressed as .alpha.F, the following equation is established; EQU VB4,5+VBE4+(Ic5/.alpha.F)RE-VBE5=0 (1)
In Eq. (1), if kT/q=VT, where k is Boltzmann's constant, T is an absolute temperature, and q is a unit electron charge, then, there exists the following relationships between the VT and the base voltages VBE4 and VBE5 of respective transistors TR4 and TR5: EQU VBE4&gt;&gt;VT, VBE5&gt;&gt;VT.
In addition, if saturation currents of the differential transistor pair TR4 and TR5 are respectively expressed as Is4 and Is5, the following equations are satisfied as; EQU VBE4=VT.multidot.1n(Ic4/Is4) (2) EQU VBE5=VT.multidot.1n(Ic5/Is5) (3)
Here, by substituting Eqs. (2) and (3) into Eq. (1) and supposing that the transistors TR4 and TR5 are identical (i.e., as Is4=Is5), Eq. (1) may be explained as follow: EQU VB4,5+VT.multidot.1n(Ic4/Ic5)+(Ic5/.alpha.F)RE=0 (4)
On the other hand, there exists the following relationship between the current I0 to be flowed into the resistor R1 and the collector currents Ic4 and Ic5: EQU .alpha.F.multidot.I0=Ic4+Ic5 (5)
Hence, by eliminating Ic4 using Eq. (5), Eq. (4) may be explained by the following: EQU VB4,5+VT.multidot.1n[(.alpha.F.multidot.I0/Ic5)-1]+(Ic5/.alpha.F)RE=0(6)
Next, in order to obtain the slope of a curve showing the change of the collector current Ic5 with the change in inter-base voltage VB4,5 of the differential transistor pair TR4 and TR5, the Ic5 in Eq. (6) is differentiated with respect to VB4,5, and the following equation may be obtained: ##EQU1##
The absolute value of Eq. (7) can be maximized when the denominator becomes minimum, that is, in case of being established the following equation (the same manner may be used with respect to Ic4): EQU Ic5=Ic4=(1/2) .alpha.F.multidot.I0 (8)
Thus, the maximum absolute value may satisfy the following equation: ##EQU2##
An inter-base voltage VB4,5 in this case becomes as follows: EQU VB4,5=(-1/2)RE.multidot.I0 (10)
FIG. 2 shows a relation of a voltage between the bases VB4,5 and the collector current Ic5. As seen from FIG. 2, in order to obtain a half-wave rectification characteristic in the conventional logarithmic amplification circuit as described above, the inter-base voltage VB4,5 is required to be provided with a voltage offset of about 4VT (about 100 mV). Therefore; using the conventional logarithmic amplification circuit it is unavoidably necessary to have a circuit for providing a voltage offset to the differential input voltage (VB4,5), which means that there exists such a problem that not only the input circuit is complicated, but also to dynamic range is difficult to be expanded. In addition, it utilizes the half-wave rectification characteristic, resulting in arising a problem that amplification is difficult to be carried out with high accuracy.
Thus, an object of this invention is to provide a logarithmic amplification circuit which has a simple input circuit and a wide dynamic range as compared with conventional ones.
Another object of this invention is to provide a logarithmic amplification circuit capable of performing high accuracy amplification.